El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$- \sin{\left(x \right)} + \cos{\left(2 x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{\pi}{2}$$
$$x_{2} = \frac{\pi}{6}$$
$$x_{3} = \frac{5 \pi}{6}$$
Solución numérica$$x_{1} = -95.8185760435073$$
$$x_{2} = -12.0427718387609$$
$$x_{3} = 61.2610569380464$$
$$x_{4} = 44.5058959258554$$
$$x_{5} = 98.9601683847854$$
$$x_{6} = -32.98672341235$$
$$x_{7} = -22.5147473507269$$
$$x_{8} = 46.6002910282486$$
$$x_{9} = -20.4203520418601$$
$$x_{10} = 92.6769826185806$$
$$x_{11} = 34.0339204138894$$
$$x_{12} = 10.9955740992967$$
$$x_{13} = -95.8185758681551$$
$$x_{14} = 2.61799387799149$$
$$x_{15} = -5.75958653158129$$
$$x_{16} = -41.3643032722656$$
$$x_{17} = 42.4115007297604$$
$$x_{18} = 52.8834763354282$$
$$x_{19} = 92.6769830871924$$
$$x_{20} = 90.5825881785057$$
$$x_{21} = -18.3259571459405$$
$$x_{22} = 71.733032256967$$
$$x_{23} = -60.2138591938044$$
$$x_{24} = -70.6858344924983$$
$$x_{25} = -32.9867230405965$$
$$x_{26} = 31.9395253114962$$
$$x_{27} = 78.0162175641465$$
$$x_{28} = 84.2994028713261$$
$$x_{29} = -93.7241808320955$$
$$x_{30} = -1.57079642893127$$
$$x_{31} = -3.66519142918809$$
$$x_{32} = 36.1283159916529$$
$$x_{33} = -26.7035373476123$$
$$x_{34} = -66.497044500984$$
$$x_{35} = -76.9690201780717$$
$$x_{36} = -51.8362786898924$$
$$x_{37} = -83.2522055292846$$
$$x_{38} = -56.025068989018$$
$$x_{39} = -62.3082542961976$$
$$x_{40} = -87.4409955249159$$
$$x_{41} = -85.3466004225227$$
$$x_{42} = 27.7507351067098$$
$$x_{43} = 75.9218224617533$$
$$x_{44} = -49.7418836818384$$
$$x_{45} = -24.60914245312$$
$$x_{46} = -100.007366139275$$
$$x_{47} = -9.94837673636768$$
$$x_{48} = -97.9129710368819$$
$$x_{49} = 48.6946859325274$$
$$x_{50} = -45.5530935873709$$
$$x_{51} = -68.5914396033772$$
$$x_{52} = 38.2227106186758$$
$$x_{53} = 69.6386371545737$$
$$x_{54} = -35.081117965086$$
$$x_{55} = -7.85398149924071$$
$$x_{56} = 10.995574056153$$
$$x_{57} = 0.523598775598299$$
$$x_{58} = -43.4586983746588$$
$$x_{59} = 82.2050077689329$$
$$x_{60} = -79.0634151153431$$
$$x_{61} = 96.8657734856853$$
$$x_{62} = 29.8451303193672$$
$$x_{63} = 25.6563400043166$$
$$x_{64} = -89.5353907455655$$
$$x_{65} = -53.9306738866248$$
$$x_{66} = 8.90117918517108$$
$$x_{67} = -58.1194639999037$$
$$x_{68} = 73.8274274783337$$
$$x_{69} = 19.3731546971371$$
$$x_{70} = -64.4026491963026$$
$$x_{71} = -91.6297857297023$$
$$x_{72} = 54.9778712411975$$
$$x_{73} = 63.3554518473942$$
$$x_{74} = 80.1106131458253$$
$$x_{75} = 23.5619451122289$$
$$x_{76} = -16.2315620435473$$
$$x_{77} = 86.393797888715$$
$$x_{78} = 40.317105721069$$
$$x_{79} = 17.2787597959772$$
$$x_{80} = 4.71238877821279$$
$$x_{81} = -47.6474885794452$$
$$x_{82} = 94.7713783832921$$
$$x_{83} = -76.9690198122422$$
$$x_{84} = -39.2699083757319$$
$$x_{85} = 88.4881930761125$$
$$x_{86} = 67.5442422659503$$
$$x_{87} = -76.9690204511548$$
$$x_{88} = -14.1371668400256$$